Méi shì 没事 or more commonly in northern China, méi shìr /mei ʂɚ/ 没事儿. Literally méi means 'there is not' (exactly, here in the phrase 'méi shìr' it means 'there will not be'), 'shìr' means 'mishap'.
'shì‘事sometimes means 'trouble', in the colloquial saying '你摊上事儿啦 Nǐ tānshang shìr la' (which was also the title of a comic sketch among a Spring Festival (entertainment) show on CCTV) means 'You'll be in (great) trouble'.
Another meaning of ‘méi shì 没事' or 'méi shìr /mei ʂɚ/ 没事儿' is 'have no work/task having to be done', here shì事 means 'business, work'.
------- 你明天上午有事吗